On the existence, uniqueness and stability of solutions for semi-linear generalized elasticity equation with general damping term
type: Item
instance of: scholarly article
title: On the existence, uniqueness and stability of solutions for semi-linear generalized elasticity equation with general damping term
zbMATH Open document ID: 1406.35196
author: A. Rahmoune
publication date: 2017-12-18T00:00:00Z
review text: The paper deals with a semi-linear hyperbolic boundary value problem for linear elastic equations with general damping term and nonlinearities of variable exponent type. The author introduces function spaces of Sobolev type with variable exponent. Then the author proves local and global existence theorems for the weak solution. The proof is based on the Galerkin's approximations. The uniqueness of this solution is obtained by eliminating some auxiliary conditions that have been imposed by other specialists. The author shows also that any solution with nontrivial initial datum becomes stable.
reviewed by: Vyacheslav I. Maksimov
Mathematics Subject Classification ID: 35L71
Mathematics Subject Classification ID: 35L53
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 35L20
zbMATH DE Number: 6819825
zbMATH Keywords: nonlinear internal stabilization
zbMATH Keywords: generalized Lebesgue space
zbMATH Keywords: Sobolev spaces with variable exponents
MaRDI profile type: Publication
full work available at URL: s10114-017-6466-y
OpenAlex ID: W2746103950
cites work: Q4165939
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cites work: Semilinear hyperbolic boundary value problem for linear elasticity equations
cites work: A nonlinear hyperbolic problem for viscoelastic equations
DOI: 10.1007/S10114-017-6466-Y
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published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 6819825